The headphones don't fold up, but they do fold flat -- and by flat, I mean really flat. While the included carrying case is fairly large in terms of height and width, since the headphones fold so flat there isn't much depth to the package. It stows away nicely in a laptop bag or backpack, or potentially your suitcase.
The headphones have a detachable cable, which is nice, though you do have to detach that cable to get the headphones to fit properly in the case. Luckily, the headphones' designers have been thoughtful enough to include an interior pocket in the case for storing that cable.
Overall, I really liked the sound of these headphones. I tend to like well-balanced, "accurate" headphones, and the Classic fits that profile, with detailed sound and bass that's plump and pleasant but not overreaching. For closed-back headphones, the sound feels open and not canned at all. There's a bit of restraint in the treble, so you're not going to get that edgier detail of "faster," more aggressive headphones that push the treble harder. I wouldn't call these laid-back, but they're fairly warm and I tried them out with a variety of music and came away feeling that they were quite versatile. That said, if you're someone who wants headphones that can deliver a more thumping bass, the Classic may not quite satisfy you.
At $199.95, the Harman Kardon Classic headphones are fairly pricey. But when you combine their impressive fit and finish and sound quality, they actually seem fairly reasonably priced compared with the competition. I compared this model with the $199.99
For those considering Harman Kardon's step-up Bluetooth Wireless Over-Ear Headphones ($249.95), alas, I haven't tried them yet, but I'd venture to guess that the Classic earphones sound better. And despite my small quibbles about their comfort level, I have no problem recommending them.